At present, most of the folding stools in the market are designed to make the seat portion of the chair or of the stool foldable. For the stool without a backrest, it generally comprises a seat portion, a stool cover covered on the seat portion and a supporting board for supporting the shape of the seat portion. The seat portion is designed to be foldable, and when folding, it only needs to take out the supporting board and then folding the seat portion to realize the folding function of the seat portion. However, for the chair with a backrest, the backrest is non-foldable since the backrest is generally fixed to the seat portion via a fixing connection, for example bolts, and the backrest is vertical to the seat portion all the time. Therefore, after the supporting boards in the stool cover and the seat portion are taken out to fold the seat portion, it still needs a large space to store the folded chair since the backrest is non-foldable and is fixed to the seat portion.